If A : B = 11 : 7, B : C = 4 : 19 then find A : B : C.

Options

A. 33 : 21 : 76
B. 1.3849421296296
C. 44 : 28 : 133
D. 0.93677083333333

Answer

To find the ratio A : B : C given the ratios A : B = 11 : 7 and B : C = 4 : 19, we can follow these steps:

### Step 1: Write down the given ratios
We have:
- A : B = 11 : 7
- B : C = 4 : 19

### Step 2: Express B in terms of a common value
To combine these ratios, we need to express B in a common way. The value of B in both ratios must be the same.

From A : B = 11 : 7, we can express B as:
- B = 7k (where k is a common multiplier)

From B : C = 4 : 19, we can express B as:
- B = 4m (where m is another common multiplier)

### Step 3: Set the expressions for B equal to each other
Since both expressions represent B, we can set them equal:
- 7k = 4m

### Step 4: Find a common multiplier
To find a common value for k and m, we can express k and m in terms of a new variable. Let's find the least common multiple (LCM) of 7 and 4. The LCM of 7 and 4 is 28.

Now, we can express k and m:
- Let k = 4n (so that 7k = 28n)
- Let m = 7n (so that 4m = 28n)

### Step 5: Substitute k and m back into A and C
Now we can substitute back to find A and C:
- From A : B = 11 : 7, we have:
- A = 11k = 11(4n) = 44n
- B = 7k = 7(4n) = 28n

- From B : C = 4 : 19, we have:
- B = 4m = 4(7n) = 28n (which is consistent)
- C = 19m = 19(7n) = 133n

### Step 6: Write the final ratio A : B : C
Now we can write the ratio A : B : C:
- A : B : C = 44n : 28n : 133n

Since n is a common factor, we can simplify this to:
- A : B : C = 44 : 28 : 133

### Final Answer
Thus, the final ratio A : B : C is:
**A : B : C = 44 : 28 : 133**

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